MATHEMATICS HIGH SCHOOL

Ethan stands 256 cm at point C from a lamp post AB. He is 180 cm tall and his shadow from the lamp is 144 cm long. Find the height AB, in metres, of the lamp post.

Answers

Answer 1

Answer:

Answer:500 cm

Step-by-step explanation:

Given

height of ethan = 180 cm

length of shadow =144 cm

Distance of ethan from lamp =256 cm

from diagram, we can write

$\Rightarrow tan \theta =(FC)/(EC)\quad \ldots(i)$

$\Rightarrow \tan \theta =(AB)/(BE)\quad \ldots (ii)$

From (i) and (ii) we get

$\tan \theta =(FC)/(EC)=(AB)/(BE)$

$\Rightarrow (180)/(144)=(h)/(144+256)$

$\Rightarrow h=(180)/(144)* 400$

$\Rightarrow h=500\ cm$

So, height of lamp post AB is $500\ cm$

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Please solve the following quadratic equation and show your work: x^2 -x =30

Answers

Rewriting the equation as a quadratic equation equal to zero:
x^2 - x - 30 = 0
We need two numbers whose sum is -1 and whose product is -30. In this case, it would have to be 5 and -6. Therefore we can also write our equation in the factored form
(x + 5)(x - 6) = 0
Now we have a product of two expressions that is equal to zero, which means any x value that makes either (x + 5) or (x - 6) zero will make their product zero.
x + 5 = 0 => x = -5
x - 6 = 0 => x = 6
Therefore, our solutions are x = -5 and x = 6.

The product of c and 7 is greater than -27

Answers

hii, I think you forgot to add a question :)

What is the reflection image of (5, -3) across the line y = -x?

Answers

Answer:

The point (5,-3) reflection image across the line $y=-x$ is (3,-5).

Step-by-step explanation:

Given : Point (5,-3)

To find : The reflection image of given point across the line $y=-x$ ?

Solution :

The reflection across the line $y=-x$ is when both the coordinated changes its sign and position.

i.e, (x,y) across y=-x line became (-y,-x)

So, The point (5,3) reflection image across the line $y=-x$ is (3,-5).

Refer the attached figure below to see the reflection.

Therefore, (5,-3)→(3,-5)

Over the y-axis(x, y) → (−x, y) so ( -5, -3)

What is the graph of Y=2|3x-3|-4

Answers

y = 2|3x - 3| - 4
y = 2|3(x - 1)| - 4
y = 6|x - 1| - 4

The graph is a V shaped graph with vertex at (1, -4), x-intercepts at (1/3, 0) and (5/3, 0) any y intercept at (0, 2).

The number of boxes of food that six volunteers collected for the food drive is given in the table below.Number of Boxes
32
35
20
16
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What is the mean absolute deviation? Round to the nearest tenth.

Answers

Answer:

The mean absolute value is 7.7, when rounded to the nearest tenth.

Step-by-step explanation:

1.) To get the mean absolute deviation you have to find the mean first:

32 + 35 + 20 + 16 + 28 + 13 = 144 ÷ 6 = 24

2.) Then, you have to find the difference of each element in your data set that is away from the mean. Then, you have to find the absolute values of the answers:

32 - 24 = | 8 | → 8
35 - 24 = | 11 | → 11
20 - 24 = | -4 | → 4
16 - 24 = | -8 | → 8
28 - 24 = | 4 | → 4
13 - 24 = | -11 | → 11

3.) Then, you have to find the mean of the absolute values:

8 + 11 + 4 + 8 + 4 + 11 = 46 ÷ 6 = 7.6666666666666666666666666666667‬ = 7.7

Answer:

its 7.7

Step-by-step explanation:

i got it right in edg

Sarah saved $15 buying the dressat a 20%-off sale. What was the
regular price of the dress?

Answers

Answer:

$18

Step-by-step explanation:

since she saved 20% you turn the percentage into a decimal which is .20 then multiply it by 15 because that's how much she saved and you get $3 which you add to $15 and you get the regular price which is $18

The price is $18 because you change the 20% to .20 and multiply it by 15 which gives you $3and then you add which gives you your answer.

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